%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL008+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:33:01 PM UTC 2026
% Result : Theorem 3.75s 0.91s
% Output : CNFRefutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 6
% Syntax : Number of formulae : 78 ( 78 unt; 0 def)
% Number of atoms : 78 ( 77 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 187 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,conjecture,
composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c2,negated_conjecture,
~ ! [X0_2,X1_2,X2_2] : composition(X0_2,join(X1_2,X2_2)) = join(composition(X0_2,X1_2),composition(X0_2,X2_2)),
inference(negate_conjecture,[status(cth)],[c1]) ).
cnf(c3,plain,
composition(x0,join(x1,x2)) != join(composition(x0,x1),composition(x0,x2)),
inference(clausify,[status(esa)],[c2]) ).
cnf(c4,axiom,
join(X0_2,X1_2) = join(X1_2,X0_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
cnf(c5,plain,
join(composition(X4,X),composition(X4,X3)) = join(composition(X4,X3),composition(X4,X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
join(composition(X4,X3),composition(X4,X)) = join(composition(X4,X),composition(X4,X3)),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,axiom,
converse(converse(X0_2)) = X0_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
cnf(c8,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
composition(X3,X) = composition(X3,converse(converse(X))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
join(composition(X4,X),composition(X4,X3)) = join(composition(X4,X),composition(X4,converse(converse(X3)))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
converse(converse(join(composition(X4,X3),composition(X4,converse(X))))) = join(composition(X4,X3),composition(X4,converse(X))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c13,plain,
join(composition(X4,X3),composition(X4,converse(X))) = converse(converse(join(composition(X4,X3),composition(X4,converse(X))))),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
join(composition(X3,converse(X)),converse(X4)) = join(converse(X4),composition(X3,converse(X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c15,plain,
join(converse(X4),composition(X3,converse(X))) = join(composition(X3,converse(X)),converse(X4)),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,axiom,
converse(composition(X0_2,X1_2)) = composition(converse(X1_2),converse(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
cnf(c17,plain,
converse(composition(X3,converse(X))) = composition(converse(converse(X)),converse(X3)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c19,plain,
composition(converse(converse(X)),converse(X3)) = composition(X,converse(X3)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
converse(composition(X3,converse(X))) = composition(X,converse(X3)),
inference(transitivity,[status(thm)],[c17,c19]) ).
cnf(c21,plain,
converse(composition(X,converse(X3))) = composition(X3,converse(X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
composition(X3,converse(X)) = converse(composition(X,converse(X3))),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
join(composition(X3,converse(X)),converse(X4)) = join(converse(composition(X,converse(X3))),converse(X4)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,axiom,
converse(join(X0_2,X1_2)) = join(converse(X0_2),converse(X1_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
cnf(c25,plain,
converse(join(composition(X,converse(X3)),X4)) = join(converse(composition(X,converse(X3))),converse(X4)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
join(converse(composition(X,converse(X3))),converse(X4)) = converse(join(composition(X,converse(X3)),X4)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
join(composition(X,converse(X3)),X4) = join(X4,composition(X,converse(X3))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c28,plain,
converse(join(composition(X,converse(X3)),X4)) = converse(join(X4,composition(X,converse(X3)))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
join(converse(composition(X,converse(X3))),converse(X4)) = converse(join(X4,composition(X,converse(X3)))),
inference(transitivity,[status(thm)],[c26,c28]) ).
cnf(c30,plain,
join(composition(X3,converse(X)),converse(X4)) = converse(join(X4,composition(X,converse(X3)))),
inference(transitivity,[status(thm)],[c23,c29]) ).
cnf(c31,plain,
join(converse(X4),composition(X3,converse(X))) = converse(join(X4,composition(X,converse(X3)))),
inference(transitivity,[status(thm)],[c15,c30]) ).
cnf(c32,plain,
join(converse(composition(X4,X3)),composition(X,converse(X4))) = converse(join(composition(X4,X3),composition(X4,converse(X)))),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
converse(join(composition(X4,X3),composition(X4,converse(X)))) = join(converse(composition(X4,X3)),composition(X,converse(X4))),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
converse(composition(X3,X)) = composition(converse(X),converse(X3)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c35,plain,
join(converse(composition(X4,X3)),composition(X,converse(X4))) = join(composition(converse(X3),converse(X4)),composition(X,converse(X4))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,axiom,
composition(join(X0_2,X1_2),X2_2) = join(composition(X0_2,X2_2),composition(X1_2,X2_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity) ).
cnf(c37,plain,
composition(join(converse(X3),X),converse(X4)) = join(composition(converse(X3),converse(X4)),composition(X,converse(X4))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
join(composition(converse(X3),converse(X4)),composition(X,converse(X4))) = composition(join(converse(X3),X),converse(X4)),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
join(X,converse(X3)) = join(converse(X3),X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c40,plain,
join(converse(X3),X) = join(X,converse(X3)),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
composition(join(converse(X4),X3),converse(X)) = composition(join(X3,converse(X4)),converse(X)),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
join(converse(X),X3) = join(X3,converse(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c43,plain,
join(X3,converse(X)) = join(converse(X),X3),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
converse(join(X3,converse(X))) = converse(join(converse(X),X3)),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
converse(join(converse(X),X3)) = join(converse(converse(X)),converse(X3)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c46,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c47,plain,
join(converse(converse(X)),converse(X3)) = join(X,converse(X3)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
converse(join(converse(X),X3)) = join(X,converse(X3)),
inference(transitivity,[status(thm)],[c45,c47]) ).
cnf(c49,plain,
converse(join(X3,converse(X))) = join(X,converse(X3)),
inference(transitivity,[status(thm)],[c44,c48]) ).
cnf(c50,plain,
converse(join(X,converse(X3))) = join(X3,converse(X)),
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
join(X3,converse(X)) = converse(join(X,converse(X3))),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
composition(join(X4,converse(X3)),converse(X)) = composition(converse(join(X3,converse(X4))),converse(X)),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
converse(composition(X,join(X3,converse(X4)))) = composition(converse(join(X3,converse(X4))),converse(X)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c54,plain,
composition(converse(join(X3,converse(X4))),converse(X)) = converse(composition(X,join(X3,converse(X4)))),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
composition(join(X4,converse(X3)),converse(X)) = converse(composition(X,join(X3,converse(X4)))),
inference(transitivity,[status(thm)],[c52,c54]) ).
cnf(c56,plain,
composition(join(X3,converse(X4)),converse(X)) = converse(composition(X,join(X4,converse(X3)))),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
composition(join(converse(X4),X3),converse(X)) = converse(composition(X,join(X4,converse(X3)))),
inference(transitivity,[status(thm)],[c41,c56]) ).
cnf(c58,plain,
composition(join(converse(X3),X),converse(X4)) = converse(composition(X4,join(X3,converse(X)))),
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
join(composition(converse(X3),converse(X4)),composition(X,converse(X4))) = converse(composition(X4,join(X3,converse(X)))),
inference(transitivity,[status(thm)],[c38,c58]) ).
cnf(c60,plain,
join(converse(composition(X4,X3)),composition(X,converse(X4))) = converse(composition(X4,join(X3,converse(X)))),
inference(transitivity,[status(thm)],[c35,c59]) ).
cnf(c61,plain,
converse(join(composition(X4,X3),composition(X4,converse(X)))) = converse(composition(X4,join(X3,converse(X)))),
inference(transitivity,[status(thm)],[c33,c60]) ).
cnf(c62,plain,
converse(converse(join(composition(X4,X3),composition(X4,converse(X))))) = converse(converse(composition(X4,join(X3,converse(X))))),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
converse(converse(composition(X4,join(X3,converse(X))))) = composition(X4,join(X3,converse(X))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c64,plain,
converse(converse(join(composition(X4,X3),composition(X4,converse(X))))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c62,c63]) ).
cnf(c65,plain,
join(composition(X4,X3),composition(X4,converse(X))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c13,c64]) ).
cnf(c66,plain,
join(composition(X4,X),composition(X4,converse(converse(X3)))) = composition(X4,join(X,converse(converse(X3)))),
inference(substitution,[status(thm)],[c65]) ).
cnf(c67,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c68,plain,
join(X,converse(converse(X3))) = join(X,X3),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
composition(X4,join(X,converse(converse(X3)))) = composition(X4,join(X,X3)),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c71,plain,
composition(X4,join(X,X3)) = composition(X4,join(X3,X)),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
composition(X4,join(X,converse(converse(X3)))) = composition(X4,join(X3,X)),
inference(transitivity,[status(thm)],[c69,c71]) ).
cnf(c73,plain,
join(composition(X4,X),composition(X4,converse(converse(X3)))) = composition(X4,join(X3,X)),
inference(transitivity,[status(thm)],[c66,c72]) ).
cnf(c74,plain,
join(composition(X4,X),composition(X4,X3)) = composition(X4,join(X3,X)),
inference(transitivity,[status(thm)],[c11,c73]) ).
cnf(c75,plain,
join(composition(X4,X3),composition(X4,X)) = composition(X4,join(X3,X)),
inference(transitivity,[status(thm)],[c6,c74]) ).
cnf(c76,plain,
join(composition(x0,x1),composition(x0,x2)) = composition(x0,join(x1,x2)),
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
composition(x0,join(x1,x2)) = join(composition(x0,x1),composition(x0,x2)),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
$false,
inference(resolution,[status(thm)],[c3,c77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL008+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 22:50:22 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.75/0.91 Command-line arguments: --no-flatten-goal
% 3.75/0.91
% 3.75/0.91 % SZS status Theorem
% 3.75/0.91
% 3.75/0.91 % SZS output start CNFRefutation
% See solution above
% 3.75/0.95
% 3.75/0.95 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------